Abstract
We consider the Kirchhoff equation
where N ∈ {3, 4}, λ ≥ 0, the potential V is radial and f can be superlinear or aysmptotically linear at infinity. By using variational methods we obtain, for N = 4, the existence of a ground state radial solution when λ is small. The same holds for N = 3 with no restriction on λ. We also prove that, when λ → 0+, the solutions strongly converge to a solution of −Δu + V (x)u = f(u).
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The authors were partially supported by CNPq/Brazil.
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Batista, A.M., Furtado, M.F. Existence of Solution for an Asymptotically Linear Schrödinger-Kirchhoff Equation. Potential Anal 50, 609–619 (2019). https://doi.org/10.1007/s11118-018-9697-3
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DOI: https://doi.org/10.1007/s11118-018-9697-3